Energy density-based non-negative surface contributions in interior acoustics

Caglar Gurbuz, Johannes D. Schmid, Marinus Luegmair, Steffen Marburg

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Vibrating structures have received considerable critical attention as they radiate sound into enclosures where it is amplified by reflections. Surface and panel contribution analyses account for a useful tool to identify sound sources on vibrating structures. Current commercial solutions use the sound pressure at a field point inside the acoustic domain as the objective function. Usually, a bar chart of panel contributions to the sound pressure at a single point is supplied. A major drawback consists in the sound pressure strongly depending on the location of the specific field point. This is particularly the case for field point locations in regions with low sound pressure values. It is the aim of this study to formulate sound energy density-based surface contributions to evaluate the energy flow in enclosing structures. These energy-based contributions offer new insights into the properties of acoustic cavities, since they account for an integrative evaluation of the sound pressure and the particle velocity. For this purpose, the boundary element method has been applied to solve the three-dimensional Helmholtz equation for interior acoustics. In analogy to the non-negative intensity, the energy-based contributions are expressed in a quadratic form. By this means, acoustic cancellation effects due to alternating signs are bypassed. The results reveal regions with high contributions to the sound energy density at specific field points. Some of these surface regions appear almost inactive if only the contributions to the sound pressure were analyzed. The findings of this study indicate that energy-based surface contributions provide an effective quantity, particularly in regions with low sound pressure values.

Original languageEnglish
Article number116824
JournalJournal of Sound and Vibration
StatePublished - 9 Jun 2022


  • Acoustic energy density
  • Boundary element method
  • Interior acoustics
  • Surface contributions


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